Preheat oven to 350º. Mix ingredients in order given. Bake in greased 10 x 5 pan for 20 minutes. Two minutes before done, top with marshmallows. Melt, but do not brown, and spread over entire surface. While still warm, pour on icing. Cool 24 hours before cutting.
Mix 2 cups of powdered sugar, ¼ cup cocoa, 2 tablespoons of butter, 4 tablespoons of canned milk, and 1 teaspoon of vanilla in a saucepan. Heat until melted and pour over brownies.